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nlexa [21]
3 years ago
5

Divide. −425÷(−5) −2225 −825 825 2225

Mathematics
1 answer:
Alex17521 [72]3 years ago
6 0

Answer: The correct answer would be -85.


Step-by-step explanation: This is because the -5 becomes positive because it is inside parentheses.

This would make the expression: -425 ÷ 5.

-425 ÷ 5 is equal to -85.

Hope this helps and have a nice day! :)


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Step-by-step explanation:


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-x+ 2y = 10<br> -3x+By = 11
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Answer:

change the equation into one variable.

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Answer:

\begin{cases}y=-5x+1\\y=5x-4 \end{cases}

Step-by-step explanation:

Slope-intercept form of a <u>linear equation</u>:

\boxed{y=mx+b}

where:

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  • b is the y-intercept (where the line crosses the y-axis).

<u>Slope formula</u>

\boxed{\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}}

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<u>Substitute</u> the defined points into the slope formula:

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From inspection of the graph, the line crosses the y-axis at y = 1 and so the y-intercept is 1.

Substitute the found slope and y-intercept into the slope-intercept formula to create an equation for the line:

y=-5x+1

<u>Equation 2</u>

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Define two points on the line:

  • \textsf{Let }(x_1,y_1)=(1, 1)
  • \textsf{Let }(x_2,y_2)=(0, -4)

<u>Substitute</u> the defined points into the slope formula:

\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{-4-1}{0-1}=5

From inspection of the graph, the line crosses the y-axis at y = -4 and so the y-intercept is -4.

Substitute the found slope and y-intercept into the slope-intercept formula to create an equation for the line:

y=5x-4

<u>Conclusion</u>

Therefore, the system of linear equations shown by the graph is:

\begin{cases}y=-5x+1\\y=5x-4 \end{cases}

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Answer:

t=\frac{2.35-1.83}{\sqrt{\frac{0.88^2}{10}+\frac{0.54^2}{7}}}}=1.507  

p_v =P(t_{(15)}>1.507)=0.076

If we compare the p value and the significance level given \alpha=0.01 we see that p_v>\alpha so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and the group CTS, NOT have a significant higher mean compared to the Normal group at 1% of significance.

Step-by-step explanation:

1) Data given and notation

\bar X_{CTS}=2.35 represent the mean for the sample CTS

\bar X_{N}=1.83 represent the mean for the sample Normal

s_{CTS}=0.88 represent the sample standard deviation for the sample of CTS

s_{N}=0.54 represent the sample standard deviation for the sample of Normal

n_{CTS}=10 sample size selected for the CTS

n_{N}=7 sample size selected for the Normal

\alpha=0.01 represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

p_v represent the p value for the test (variable of interest)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean for the group CTS is higher than the mean for the Normal, the system of hypothesis would be:

Null hypothesis:\mu_{CTS} \leq \mu_{N}

Alternative hypothesis:\mu_{CTS} > \mu_{N}

If we analyze the size for the samples both are less than 30 so for this case is better apply a t test to compare means, and the statistic is given by:

t=\frac{\bar X_{CTS}-\bar X_{N}}{\sqrt{\frac{s^2_{CTS}}{n_{CTS}}+\frac{s^2_{N}}{n_{N}}}} (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other".

Calculate the statistic

We can replace in formula (1) the info given like this:

t=\frac{2.35-1.83}{\sqrt{\frac{0.88^2}{10}+\frac{0.54^2}{7}}}}=1.507  

P-value

The first step is calculate the degrees of freedom, on this case:

df=n_{CTS}+n_{N}-2=10+7-2=15

Since is a one side right tailed test the p value would be:

p_v =P(t_{(15)}>1.507)=0.076

We can use the following excel code to calculate the p value in Excel:"=1-T.DIST(1.507,15,TRUE)"

Conclusion

If we compare the p value and the significance level given \alpha=0.01 we see that p_v>\alpha so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and the group CTS, NOT have a significant higher mean compared to the Normal group at 1% of significance.

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